The knob is no doubt not frozen. There is a part under the machines that seems to gum up - you can heat that part with a hair dryer and it will dissolve the dried up oil. Then oil it with Tri-Flo oil.
I don't know what your part looks exactly like but it might look something like this one from my old Domestic machine - there may be a picture of a Necchi on QB in the vintage sewing machine shop if you go into search but here is the feed dog drop from my Domestic:
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